Servo control system

ABSTRACT

1. A servo system for controlling the scanning speed of a directive hemispherical search antenna, comprising in combination, first servomotor means adapted to be coupled to said antenna for rotating said antenna about a vertical axis whereby to rotate the directive axis thereof in azimuth, the speed of rotation of said antenna varying according to the magnitude of a voltage supplied to said first servomotor means, second servomotor means adapted to be coupled to said antenna for rotating said antenna about a horizontal axis whereby to rotate the directive axis thereof in elevation; the movement of said antenna about said horizontal axis varying according to the magnitude of a voltage supplied to said second servomotor means, means coupled to said second servomotor means and responsive to the movement of said antenna about said horizontal axis, said means receiving an applied voltage of constant magnitude and supplying an output voltage varying in magnitude according to the secant of the elevation angle of said antenna, means coupling said output voltage to said first servomotor means for varying the speed of said first servomotor means according to the secant of the elevation angle of said antenna, reversing switch means coupled to said second servomotor means and responsive to the movement of said antenna about said horizontal axis, means coupling said output voltage varying according to the secant of said elevation angle to said reversing switch means, and means coupling the voltage from said reversing switch means to said second servomotor means for varying the speed of said second servomotor means according to the secant of the elevation angle of said antenna, said second servomotor means and said reversing switch means causing the elevation angle of said antenna to oscillate about said horizontal axis through an angle less than 90*.

United States Patent McCartney ,{451 Dec.26, 1972 [54] SERVO CONTROLSYSTEM [72] Inventor: Earl J. McCartney, Rockville Center, N.Y.

[73] Assignee: The Sperry Rand Corp., Great Neck, N.Y.

[22] Filed: Oct. 5, 1954 [21] 'App1.No.: 460,295

[52] Cl. ....343/759, 343/766, 318/625, 318/627 [51] Int. Cl. ..H01q3/10 [58] Field of Search ..318/ 19, 282, 286, 466-468, 318/625, 627;250/33.65l; 343/117, 759

561 References Cited UNITED STATES PATENTS 2,515,248 7/1950 McCoy.........34s/ 117 2,648,040 8/1953 Schneide ....3l8/286 PrimaryExaminer-Benjamin A. Borchelt Assistant Examiner-R. KinbergAttorney-Reginald V. Craddock EXEMPLARY CLAIM axis-thereof in azimuth,the speed of rotation of said antenna varying according to the magnitudeof a volt age supplied to said first servomotor'means, second servomotormeans adapted to be coupled to said antenna for rotating said antennaabout a horizontal axis whereby to rotate the directive axis thereof inelevation; the movement of said antenna about said horizontal axisvarying according to the magnitude of a voltage supplied to said secondservomotor means, means coupled to said second servomotor means andresponsive to the movement of said antenna about said horizontal axis,said means receiving an applied voltage of constant magnitude andsupplying an output voltage varying in magnitude according to the secantof the elevation angle of said antenna, means coupling said outputvoltage to said first servomotor means for varying the speed of saidfirst servomotor means according to the secant of the elevation angle ofsaid antenna, reversing switch means coupled to said second servomotormeans and responsive to the movement of said antenna about saidhorizontal axis, means coupling said output voltage varying according tothe secant of said elevation angle to said reversing 12 Claims, 3Drawing Figures 16 I3 39 w 20 19 as Z/ /5 4 M GEN. s: a/z 1 4 417 i 4 ,7er

.42. an 0/: SERVO as m 23 R ta eggs 33 5 27 26 SERVO CONTROL SYSTEM Thepresent invention relates to servo control systems, and in particular toa servo system for controlling a hemispherical search antenna.

ln pending application Ser. No. 517,008, filed Jan. 5, 1944, now U.S.Pat. No. 2,784,402, issued Mar. 5, 1957, in the names of G. E. White andD. S. Pensyl, en-

titled Control-Systemsf and assigned to the same as- I signee as thepresent invention, there is described and claimed a'servo-controlledtracking antenna system in which the response of the servo systemcontrolling the antenna in azimuth varies according to the secant of theelevation angle of the directive axis'of the antenna. Thisservo-controlled antenna system provides improved automatic tracking bycompensating the azimuth servo control system for the loss in angularsensitivity of the azimuth error detector at high elevation angles ofthe directive antenna. j

The present invention is related to the above-mentioned application andis chiefly concerned with a servo-controlled directive antenna forspirally searching the hemisphere as quickly as possible'and withuniform coverage of eachelement of space to insure early detection ofthe presence of targets.

Accordingly, the principal object of the present invention is to providea highly efficient, rapid scanning hemispherical search antenna system.

Another object of the invention is to provide a directive antenna systemfor spirally searching the hemisphere in a minimum of time.

Still another object is to provide a search antenna system that isuniformly responsive to each element of space in a hemisphere.

In accordance with the present invention there is introduced a directiveantenna system for spirally scanning a hemisphere including a servosystem for controlling the rotation of the directive antenna about avertical axis, and a servo system for controlling the oscillation of theantenna in elevation. To achieve the objects of the invention the speedof rotation and the rate of oscillation of the antenna is variedaccording to the secant of the elevation angle as the elevation anglevaries over a range from to approximately 75. A limit switch is providedto reverse the direction of motion of the elevation servo system whenthe elevation angle is equal to approximately 75 and again when theelevation angle is equal to 0 to produce the desired oscillation of thepointing axis of the antenna.

The above objects of and the brief introduction to the present inventionwill be more fully understood and further objects and advantages willbecome apparent from a study of the following detailed description inconnection with the drawing, wherein,

FIG. 1 illustrates a block diagram of the servo-controlled hemisphericalsearch antenna system of the present invention,

FIG. 2 is a curve of the secant of the elevation angle of the antennasystem, and

FIG. 3 is a representation of a beam spirally scanning a hemisphere.

Referring to FIG. 1, antenna housing 11 mounted on shaft 12 is supportedby'yoke 13. The antenna housing 11 may contain a directive paraboloidalradar antenna or a suitable infra-red antenna and detector element. Aworm wheel 14 is attached to one end of shaft 12 and is driven by wormgear 15 and shaft 16 to vary the directive axis of the antenna inelevation about the horizontal axis definedby shaft 12. Shaft 16 iscoupled in driving relation to shaft 17 through spur gears 18 and 19respectively. Yoke 13 is mounted on a circular platform 20 whose rimcontains teeth engaged with spur gear 21. The spur gear 21 is driven byshaft 22 to rotate platform 20 and housing 11 about a vertical axiscoinciding with the longitudinal axis of shaft 17.

I A two-phase elevation servomotor 23 coupled to a threaded shaft 24drives shaft 17 through a differential 25. A two-phase azimuthservomotor 26 coupled to shaft 27 drives shaft 22 through bevel gears 28and 29, and drives shaft 17 through the differential 25. Thedifferential 25 prevents the rotation of shaft 16, and accordinglythemovement of the directive axis of the antenna in elevation, as theazimuth servomotor drives the platform 20 and antenna housing 11 about avertical axis. The movement of the housing 11 in elevation about thehorizontal axis defined by shaft 12, and hence the directive axis of theantenna in elevation, is varied according to the magnitude andphase ofacontrol voltage supplied to elevation servomotor 23. The. speed ofrotation of antenna housing 11 about the vertical axis varies accordingto the magnitude of a control voltage supplied to azimuth servomotor 26.

Wiper arm 30 of a secant potentiometer 31 is coupled by shaft 32 andbevel gears 33 and 34 to the threaded shaft 24. The winding of thesecant potentiometer is supplied with an alternating voltage of constantmagnitude obtained from a manually adjustable potentiometer 35.Potentiometer 35 is supplied with an alternating voltage e, obtainedfrom an external reference generator. Resistor 36 cooperates with thesecant potentiometer 31 to provide a finite output voltage between thewiper arm of the secant potentiometer and ground when the arm issituated at one end of its range of travel. The alternating outputvoltage between the wiper arm 30 and groundis supplied to the input ofelevation servo amplifier 37 and to the input of azimuth servo amplifier38.

A cross-field eddy current generator 39 is coupled through spur gears40, 41, 42, and 43 to the threaded shaft 24. The generator produces analternating output voltage at the frequency of the reference voltage e,.The magnitude of the generated voltage varies accord ing to the speed ofrotation of shaft 24 coupled to servomotor 23, and the phase of thegenerated voltage depends upon the direction of rotation of shaft 24.Similarly, a cross-field eddy current generator 44 is coupled throughspur gears 45, 46, 47, and 48 to shaft 27. The alternating outputvoltage from generator 44 varies in magnitude according to the speed ofrotation of shaft 27 coupled to azimuth servomotor 26.

The alternating output voltage from generator 39 is applied as a speedfeedback voltage to the input of elevation servo amplifier 37 in phaseopposition to the alternating voltage obtained from the secantpotentiometer 31. The difference voltage is amplified by the elevationservo amplifier, and is supplied through a reversing switch 47 to theinput of elevation servomotor 23. The phase of this difference voltageis established by the larger of the two opposing applied voltages. Thespeed feedback voltage is employed to insure that the speed of theelevation servomotor is controlled according to the magnitude of thealternating voltage obtained from the secant potentiometer.

Reversing switch 49 is actuated by the guided nut ,50

on threaded shaft 24 at each extreme of its'travel to reverse the phaseof the amplified output voltage applied to elevation servomotor 23, and,accordingly, the direction of rotation of shaft 24. This phase reversaloccurs when the elevation angle of the directive axis is approximatelyand 75. Accordingly, the directive axis of the antenna oscillates inelevation between the angles of approximately 0 and 75.

The alternating output voltage from the eddy current generator 44 isapplied as a feedback voltage to the input of azimuth servo amplifier 38in phase opposition to the voltage obtained from secant potentiometer31'. The difference voltage is amplified by azimuth servo amplifier 38and supplied to azimuth servomotor 26.

The speed of elevation servomotor 23 and azimuth servo-motor 26 isdetermined by the magnitude of the alternating control voltage appliedto these servomotors. The magnitude of the applied voltage variesaccording to the secant of the elevation angle of the antenna asillustrated in FIG. 2. Accordingly, as the directive axis of the antennamoves to search the hemisphere, it moves faster in both azimuth andelevation as the directive axis approaches the zenith.

The control of the speed of the antenna as a function of the secant ofthe elevation angle provides uniform coverage of each element ofspace ina hemisphere in a minimum of time. This may be understood by referringto the representation of a beam spirally searching a hemisphereillustrated in FIG. 3. The peripheral scanning speed of the beam on theimaginary surface of the hemisphere at the horizon is determined by theangular velocity of the beam about the vertical axis and the diameter ofthe hemisphere. As the axis of the scanning beam is increased inelevation, the peripheral distance covered for each revolution of thebeam is reduced according to the cosine of the elevation angle.Accordingly, with a constant angular velocity about the vertical axis,the peripheral scanning speed is reduced as the elevation angleincreases. To achieve uniform coverage of each element of space in ahemisphere it is desirable to scan each element of area on the imaginarysurface of the hemisphere in the same amount of time. ln other words, itis desirable to provide-a constant peripheral scanning speed of the beamrather than a constant angular'velocity about the vertical axis. Toprovide a constant peripheral scanning speed in azimuth, the angularvelocity of the beam must be varied according to the inverse of thecosine of the elevation angle, or according to the secant of theelevation angle. For example, the angular velocity of the beam about thevertical axis at an elevation angle of 60 must be twice the angularvelocity at the horizon since the beam will have only one-half theperipheral distance to scan. At an elevation angle of 75, the angularvelocity will be almost four times the angular velocity at the horizonin order to maintain a constant peripheral speed in azimuth. Expresseddifferently, the angular velocity must be varied according to thecasecant of the angle between the directive axis of the antenna and thevertical axis.

With the higher angular velocities provided as the directiveaxis of theantenna approaches the zenith, the time required for the beam to rotateabout the vertical axis reduces. Accordingly, to maintain a constantoverlap of the swaths of the beam, it is necessary to increase thescanning speed in elevation as the scanning speed in azimuth increases.Thus, the directive axis must be moved in elevation at a speedproportional to the secant of the instantaneous elevation angle.

The azimuth and elevation scanning speeds needed to search a hemisphereare determined by the width in elevation of the scanningbeam, the amountof overlap of the swaths, and the speed capabilitiesof the two servosystems. With a scanning beam having a 3 width in elevation and a 20percent overlap of the swaths, the beam searches 2.4 in elevation foreach revolution in azimuth. Accordingly, the azimuth scanning speed mustbe fasterthan the elevationscanning speedin the ratio of 360 to 2.4,i.e., 150:1. .This ratio of scanning speeds remains constant atall'elevation' angles. For a selected upper elevation angular limit of 75, the azimuth scanning speed will be a maximum at this elevation angleand will be limited by the speed capabilities of the azimuth servosystem. Once the azimuth scanning speed at this elevation angle ischosen, the elevation scanning speed is determined by dividing theazimuth scanning speed by 150. The scanning speeds reduce as theelevation angle reduces in accordance with'the secant of the elevationangle, as illustrated in FIG. 2.

The present invention accomplishes the desired hemispherical search upto elevation angles of approximately 75. Since the secant of theelevation angle approaches infinity at the zenith, it is not possible toscan the entire hemisphere according to the secant of the elevationangle.

Since many changes could be made in the above construction and manyapparently widely different embodiments of this invention could be madewithout departing from the scope thereof, it is intended that all mattercontained in the above description or shown in the accompanying drawingsshall be interpreted as illustrative and not in a limiting sense.

What is claimed is:

l. A servo system for controlling the scanning speed of a directivehemispherical search antenna, comprising in combination, firstservomotor means adapted to be coupled to said antenna for rotating saidantenna about a vertical axis whereby to rotate the directive axisthereof in azimuth, the speed of rotation of said antenna varyingaccording to the magnitude of a voltage supplied to said firstservomotor means, second ser' vomotor means adapted to be coupled tosaid antenna for rotating said antenna about a horizontal axis wherebyto rotate the directive axis thereof in elevation, the movement of saidantenna about said horizontal axis varying according to the magnitude ofa voltage supplied to said second servomotor means, means coupled'tosaid second servomotor means and responsive to the movement of saidantenna about said horizontal axis, said means receiving an appliedvoltage of con- 'stant magnitude and supplying an output voltagevarysecant of the elevation angle of said antenna, reversing switchmeans coupled to said second servomotor means and responsive to themovement of said antenna about said horizontal axis, means coupling saidoutput voltage varying according to the secant of said elevation angleto said reversing switch means, and means coupling the voltage from saidreversing switch means servomotor means and said reversing switch meanscausing the elevation angle of said antenna to oscillate about saidhorizontal axis through an angle less than 90.

2. In combination, .a shaft adapted to be rotated about a vertical axisand whose angular position is adapted to be oscillated about itslongitudinal axis, the longitudinal axis of said shaft extendingperpendicular to said vertical axis, first servomotor means coupled tosaid shaft for rotating said shaft about said vertical axis in responseto an applied signal, the rotational speed of said shaft varyingaccording to the magnitude of said applied signal, second servomotormeans coupled to said shaft for varying the angular position thereofabout its longitudinal axis in response to an applied signal, themovement in angular position of said shaft varying according to themagnitude of an applied signal, means coupled to said shaft for movementtherewith about its longitudinal axis, said means receiving an inputsignal of fixed magnitude and providing an'output signal varying inmagnitude according to the secant function of the angular position ofsaid shaft about its longitudinal axis, means coupling said outputsignal to saidfirst servomotor means for varying the movement of saidshaft about said vertical axis in accordance with said secant function,reversing switch means coupled to said shaft and responsive to itsangular position, means coupling said output signal to said reversingswitch means, and means coupling the signal from said reversing switchmeans to said second servo motor means, said second servomotor means andsaid reversing switch means causing the angular position of said shaftto oscillate about its longitudinal axis the oscillatory movementthereof about its longitudinal axis also varying in accordance with saidsecant-function.

3. ln combination, a directive antenna adapted to be rotated in azimuthabout a vertical axis and whose directive axis is adapted to be variedin elevation about a horizontal axis, whereby said directive axis may becontrolled spirally to scan a hemisphere, first servomotor means coupledto said directive antenna for rotating said antenna about said verticalaxis, the speed of rotation of said antenna varying according to themagnitude of an applied voltage, second servomotor means coupled to saidantenna for varying the directive axis thereof in elevation, themovement of the directive axis of said antenna in elevation varyingaccording to the magnitude of an applied voltage, means responsive tomovement of the directive axis of said antenna in elevation andreceiving an applied voltage of constant magnitude for providing anoutput voltage varying in magnitude according to the secant of theelevation angle of thedirective axis of said antenna, and meanssupplying said outputvoltage to said first and second servomotor meansfor respectively controlling the speeds thereof in accordance with saidoutput voltage.

4. In combination, a directive antenna adapted to be rotated about afirst axisxand whose directive axis is adapted to be varied about asecond axis perpendicular to said first axis, the directive axis of saidantenna extending perpendicular to said second axis, first servomotormeans coupled to said directive antenna forv rotating said antenna aboutsaid first axis, the speed of rotation of said antenna varying accordingto the magnitude of an applied signal, second servomotor means coupledto said antenna for varying the directive axis of said antenna aboutsaid second axis, the movement of the directive axis of said antennaabout said second axis varying according to the magnitude of an appliedsignal, means responsive to movement of said directive axis about saidsecond axis for providing an output signal varying in magnitudeaccording to the cosecant of the angle between said first axis and thedirective axis of said antenna, and means applying said output voltageto said first and second servomotor means.

I 5. in combination, a body adapted to be moved about a first axis andabout a second axis perpendicular to said first axis, first servomotormeans coupled to said body for varying the movement thereof about'saidfirst axis according to the speed of said first servomotor, secondservomotor means coupled to said body for varying the movement thereofabout said second axis according to the speed of said second servomotor,and means coupled to said body and responsive to the movement thereofabout said second axis, said lastmentioned means being further coupledto said first and second servomotor means for varying the speeds of bothsaid first and second servomotors in accordance with'the cosecant of theangle of movement of said body about said second axis relative to saidfirst axis.

6. The apparatus as defined in claim 5 further comprising means coupledto said body and responsive to the angular movement thereof about saidsecond axis, said means being coupled to said second servomotor meansfor periodically reversing the direction of rotation of said secondservomotor when the angular movement of said body about said second axisvaries through a predetermined angle less than 7. A servo control systemfor moving a body about first and second, mutually perpendicular axesaccording to its motion about said second axis, comprising incombination, a first servomotor means coupled to said body for varyingthe movement thereof about said first axis according to the speed ofsaid first servomotor,

second servomotor means coupled to said body .for

varying the movement thereof about said second axis according to thespeed of said second servomotor, and means coupled to said secondservomotor means and responsive to the movement of said body about saidsecond axis for varying the speed of said first and second servomotors,the speed of said first and second servomotors varying according to thecosecant of the angle of movement of said body about said second axisrelative to said first axis.

8. The servo control system as defined in claim 7 further comprisingmeans coupled to said body and responsive to the angular movementthereof about said second axis for periodically reversing the directionof rotation of said second servomotor means when the angular movement ofsaid body about said second axis varies through a predetermined angularrange.

9. In combination, a body adapted to be moved about a first axis andabout a second axis perpendicular to said first axis, servomotor meanscoupled to said body for varying the movement thereof about said firstand second axesaccording to the speed of said servomotor means, themovement of said body about said first axis being appreciably fasterthan the movement thereof about said second axis, and means coupled tosaid body and responsive to the movement thereof about said second axisfor varying the speed of said servomotor means, said means varying thespeed of said servomotor means according to the cosecant function of theangle of movement of said body about said second axis relative to saidfirst axis whereby to control the movement of said body about both saidfirst and second axes in accordance with said cosecant function.

10. In combination, a body adapted to be moved 7 about first and secondmutually perpendicular axes, servomotor means coupled to said body forvarying the movement thereof about said second axis, and means coupledto said body and responsive to the movement thereof about said secondaxis for varying the speed of said servomotor means according to thecosecant function of the angle of movement of said body about saidsecond axis relative to said first axis whereby to vary the speed ofmovement of said body about said second axis in accordance with saidcosecant function.

11. In a scanning system for an antenna, a first signalresponsiveservomotor means for continuously rotating said antenna in azimuth, asecond signal-responsive ser vomotor means for cyclically, rotating saidantenna in elevation between predetermined angular limits, the speed ofcontinuous rotation of said antenna in azimuth being substantiallygreater than the cyclic speed of rotation of said antenna in elevationwhereby the directive axis of said antenna is caused spirally to scan ahemisphere, means for continuously producing a signal proportionalwithin predetermined angular limits to the secant of the angle ofelevation of said antenna during each cycle of rotation thereof inelevation, means for supplying said signal to said first servomotorthereby continuously to vary the speed of rotation of said antenna inazimuth in accordance with said signal, and means for supplying saidsignalvto said second servomotor for continuously varying the speed ofrotation of said antenna between said angular limits in elevation inaccordance with said signal whereby to cause said an tenna uniformly toscan each element of space in said hemisphere in a minimum of scanningtime in eleva-- tion.

12. In a scanning system by means of which the directive axis of anantenna may be caused to scan a hemisphere, a first single-responsivemeans for continuously rotating the directive axis of said antenna inazimuth in the same direction, a second signal responsive means forcyclically rotating the directive axis of said antenna in elevationbetween predetermined angueach cycle of rotation thereof in elevation,means for supplying said signal to said first means thereby continuouslyto vary the speed of rotation of said directive axis in azimuth in acerdance with s aid signal, and means for simultaneous y supplying saidsignal to said second means for continuously varying the speed ofrotation of said directive axis between said angular limits in elevationin accordance with said signal whereby to cause said directive axisuniformly to scan each element of space in said hemisphere in a minimumof scanning time in elevation.

nnnn Us

1. A servo system for controlling the scanning speed of a directivehemispherical search antenna, comprising in combination, firstservomotor means adapted to be coupled to said antenna for rotating saidantenna about a vertical axis whereby to rotate the directive axisthereof in azimuth, the speed of rotation of said antenna varyingaccording to the magnitude of a voltage supplied to said firstservomotor means, second servomotor means adapted to be coupled to saidantenna for rotating said antenna about a horizontal axis whereby torotate the directive axis thereof in elevation, the movement of saidantenna about said horizontal axis varying according to the magnitude ofa voltage supplied to said second servomotor means, means coupled tosaid second servomotor means and responsive to the movement of saidantenna about said horizontal axis, said means receiving an appliedvoltage of constant magnitude and supplying an output voltage varying inmagnitude according to the secant of the elevation angle of saidantenna, means coupling said output voltage to said first servomotormeans for varying the speed of said first servomoTor means according tothe secant of the elevation angle of said antenna, reversing switchmeans coupled to said second servomotor means and responsive to themovement of said antenna about said horizontal axis, means coupling saidoutput voltage varying according to the secant of said elevation angleto said reversing switch means, and means coupling the voltage from saidreversing switch means to said second servomotor means for varying thespeed of said second servomotor means according to the secant of theelevation angle of said antenna, said second servomotor means and saidreversing switch means causing the elevation angle of said antenna tooscillate about said horizontal axis through an angle less than 90*. 2.In combination, a shaft adapted to be rotated about a vertical axis andwhose angular position is adapted to be oscillated about itslongitudinal axis, the longitudinal axis of said shaft extendingperpendicular to said vertical axis, first servomotor means coupled tosaid shaft for rotating said shaft about said vertical axis in responseto an applied signal, the rotational speed of said shaft varyingaccording to the magnitude of said applied signal, second servomotormeans coupled to said shaft for varying the angular position thereofabout its longitudinal axis in response to an applied signal, themovement in angular position of said shaft varying according to themagnitude of an applied signal, means coupled to said shaft for movementtherewith about its longitudinal axis, said means receiving an inputsignal of fixed magnitude and providing an output signal varying inmagnitude according to the secant function of the angular position ofsaid shaft about its longitudinal axis, means coupling said outputsignal to said first servomotor means for varying the movement of saidshaft about said vertical axis in accordance with said secant function,reversing switch means coupled to said shaft and responsive to itsangular position, means coupling said output signal to said reversingswitch means, and means coupling the signal from said reversing switchmeans to said second servo motor means, said second servomotor means andsaid reversing switch means causing the angular position of said shaftto oscillate about its longitudinal axis the oscillatory movementthereof about its longitudinal axis also varying in accordance with saidsecant function.
 3. In combination, a directive antenna adapted to berotated in azimuth about a vertical axis and whose directive axis isadapted to be varied in elevation about a horizontal axis, whereby saiddirective axis may be controlled spirally to scan a hemisphere, firstservomotor means coupled to said directive antenna for rotating saidantenna about said vertical axis, the speed of rotation of said antennavarying according to the magnitude of an applied voltage, secondservomotor means coupled to said antenna for varying the directive axisthereof in elevation, the movement of the directive axis of said antennain elevation varying according to the magnitude of an applied voltage,means responsive to movement of the directive axis of said antenna inelevation and receiving an applied voltage of constant magnitude forproviding an output voltage varying in magnitude according to the secantof the elevation angle of the directive axis of said antenna, and meanssupplying said output voltage to said first and second servomotor meansfor respectively controlling the speeds thereof in accordance with saidoutput voltage.
 4. In combination, a directive antenna adapted to berotated about a first axis and whose directive axis is adapted to bevaried about a second axis perpendicular to said first axis, thedirective axis of said antenna extending perpendicular to said secondaxis, first servomotor means coupled to said directive antenna forrotating said antenna about said first axis, the speed of rotation ofsaid antenna varying according to the magnitude of an applied signal,second servomotor means coupled tO said antenna for varying thedirective axis of said antenna about said second axis, the movement ofthe directive axis of said antenna about said second axis varyingaccording to the magnitude of an applied signal, means responsive tomovement of said directive axis about said second axis for providing anoutput signal varying in magnitude according to the cosecant of theangle between said first axis and the directive axis of said antenna,and means applying said output voltage to said first and secondservomotor means.
 5. In combination, a body adapted to be moved about afirst axis and about a second axis perpendicular to said first axis,first servomotor means coupled to said body for varying the movementthereof about said first axis according to the speed of said firstservomotor, second servomotor means coupled to said body for varying themovement thereof about said second axis according to the speed of saidsecond servomotor, and means coupled to said body and responsive to themovement thereof about said second axis, said last-mentioned means beingfurther coupled to said first and second servomotor means for varyingthe speeds of both said first and second servomotors in accordance withthe cosecant of the angle of movement of said body about said secondaxis relative to said first axis.
 6. The apparatus as defined in claim 5further comprising means coupled to said body and responsive to theangular movement thereof about said second axis, said means beingcoupled to said second servomotor means for periodically reversing thedirection of rotation of said second servomotor when the angularmovement of said body about said second axis varies through apredetermined angle less than 90*.
 7. A servo control system for movinga body about first and second, mutually perpendicular axes according toits motion about said second axis, comprising in combination, a firstservomotor means coupled to said body for varying the movement thereofabout said first axis according to the speed of said first servomotor,second servomotor means coupled to said body for varying the movementthereof about said second axis according to the speed of said secondservomotor, and means coupled to said second servomotor means andresponsive to the movement of said body about said second axis forvarying the speed of said first and second servomotors, the speed ofsaid first and second servomotors varying according to the cosecant ofthe angle of movement of said body about said second axis relative tosaid first axis.
 8. The servo control system as defined in claim 7further comprising means coupled to said body and responsive to theangular movement thereof about said second axis for periodicallyreversing the direction of rotation of said second servomotor means whenthe angular movement of said body about said second axis varies througha predetermined angular range.
 9. In combination, a body adapted to bemoved about a first axis and about a second axis perpendicular to saidfirst axis, servomotor means coupled to said body for varying themovement thereof about said first and second axes according to the speedof said servomotor means, the movement of said body about said firstaxis being appreciably faster than the movement thereof about saidsecond axis, and means coupled to said body and responsive to themovement thereof about said second axis for varying the speed of saidservomotor means, said means varying the speed of said servomotor meansaccording to the cosecant function of the angle of movement of said bodyabout said second axis relative to said first axis whereby to controlthe movement of said body about both said first and second axes inaccordance with said cosecant function.
 10. In combination, a bodyadapted to be moved about first and second mutually perpendicular axes,servomotor means coupled to said body for varying the movement thereofabout said second axis, and means coupled to said body and responsive tothe movement thereof about said second axis for varying the speed ofsaid servomotor means according to the cosecant function of the angle ofmovement of said body about said second axis relative to said first axiswhereby to vary the speed of movement of said body about said secondaxis in accordance with said cosecant function.
 11. In a scanning systemfor an antenna, a first signal-responsive servomotor means forcontinuously rotating said antenna in azimuth, a secondsignal-responsive servomotor means for cyclically rotating said antennain elevation between predetermined angular limits, the speed ofcontinuous rotation of said antenna in azimuth being substantiallygreater than the cyclic speed of rotation of said antenna in elevationwhereby the directive axis of said antenna is caused spirally to scan ahemisphere, means for continuously producing a signal proportionalwithin predetermined angular limits to the secant of the angle ofelevation of said antenna during each cycle of rotation thereof inelevation, means for supplying said signal to said first servomotorthereby continuously to vary the speed of rotation of said antenna inazimuth in accordance with said signal, and means for supplying saidsignal to said second servomotor for continuously varying the speed ofrotation of said antenna between said angular limits in elevation inaccordance with said signal whereby to cause said antenna uniformly toscan each element of space in said hemisphere in a minimum of scanningtime in elevation.
 12. In a scanning system by means of which thedirective axis of an antenna may be caused to scan a hemisphere, a firstsingle-responsive means for continuously rotating the directive axis ofsaid antenna in azimuth in the same direction, a second signalresponsive means for cyclically rotating the directive axis of saidantenna in elevation between predetermined angular limits, the speed ofrotation of said directive axis in azimuth being substantially greaterthan the cyclic speed of rotation of said directive axis in elevationwhereby said directive axis is caused spirally to scan said hemisphere,means for producing a signal proportional within predetermined angularlimits to the secant of the angle of elevation of said directive axisduring each cycle of rotation thereof in elevation, means for supplyingsaid signal to said first means thereby continuously to vary the speedof rotation of said directive axis in azimuth in accordance with saidsignal, and means for simultaneously supplying said signal to saidsecond means for continuously varying the speed of rotation of saiddirective axis between said angular limits in elevation in accordancewith said signal whereby to cause said directive axis uniformly to scaneach element of space in said hemisphere in a minimum of scanning timein elevation.